https://support.google.com/groups/answer/1191206?hl=en
Copy and paste the HTML (written below in green). Make sure you paste it where you would like your forum to show on your site. Important: In the HTML, make sure to change "forum-name" to the name of your group. The text you need to replace is written in red below.
<iframe id="forum_embed"
src="javascript:void(0)"
scrolling="no"
frameborder="0"
width="900"
height="700">
</iframe>
<script type="text/javascript">
document.getElementById("forum_embed").src =
"https://groups.google.com/forum/embed/?place=forum/forum-name" +
"&showsearch=true&showpopout=true&parenturl=" +
encodeURIComponent(window.location.href);
</script>
